I'm studying multi variable calculus, we are researching about cylinders. And my teacher says that there are not only cylinders with a circular base, that there can be cylinders with a triangular base (which according to me are prisms) or open cylinders (defined by $z = x ^ 2$ for example).
Is this info correct?
On
Cylindrical Surface is a curved surface which we get by parallel translation of a line, the generating line or generator along a curve, the so-called directing curve (Fig. 1).
Cylinder is a solid bounded by a cylindrical surface with a closed directing curve, and by two parallel bases cut out from two parallel planes by the cylindrical surface.
Figure 1:
Yes it is a cylinder (i.e. a cylindrical surface) with the parabola $z=x^2$ as right section (directrix) traced out along $y$ axis (generatrix).
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